Such a deal would satisfy neither supporters nor opponents of the coalition.

The coalition is now likely to end before 2014. Photograph: Getty Images.

The idea of a "confidence and supply" agreement between the Conservatives and the Liberal Democrats, first mooted after the 2010 election, has re-entered political discussion after the almighty bust-up over House of Lords reform[3]. The expectation on both sides is that the coalition will end in 2014, a year out from the next election, or possibly even earlier. Conservative MP Graham Brady, the chairman of the 1922 committee, told Radio 4's Westminster Hour[4] last night:

I think it would be logical and sensible for both parties to be able to present their separate vision to the public in time for the public to form a clear view before the election.

Of course, it is always possible that that moment of separation could come sooner. It's very difficult to predict when that might be.

The Lib Dems would then agree to support a minority Tory government in votes of no confidence ("confidence") and on any Budget (or "supply") measure.

It's arguable that the Lib Dems should have adopted such an arrangement from the start, rather than entered coalition with the Conservatives. Whilst Nick Clegg's party would still have had to support George Osborne's "emergency Budget" and the Spending Review, it could have avoided breaking its totemic pledge to cap tuition fees and could have voted against the government's NHS reforms.

But a confidence and supply deal with the Tories would now be the worst of all possible worlds for the Lib Dems. It would do nothing to placate those voters who despise them for propping up a Conservative government (indeed, this charge would have even more resonance), whilst antagonising those who believe they were right to enter coalition "in the national interest". Clegg's party would still have to vote for a Conservative Budget, brimming with welfare cuts, with even less guarantee of concessions elsewhere. A pact with the Tories would, to borrow a phrase, be a "miserable little compromise[5]".

There are good arguments for the Lib Dems remaining in the coalition until 2015 and for them withdrawing completely before the next election. But there are none for entering the purgatory of confidence and supply.

Update: Academic Tim Bale, the author of the excellent The Conservative Party from Thatcher to Cameron, has alerted me[6] to his research[7] on the subject, which confirms that "confidence and supply" is frequently a curse for small parties.